Infrared and NMR Spectroscopic Fingerprints of theAsymmetric H7

+O3 Complex in SolutionEve Kozari,[a] Mark Sigalov,[a] Dina Pines,[a] Benjamin P. Fingerhut,[b] and Ehud Pines*[a]

Infrared (IR) absorption in the 1000–3700 cm� 1 range and1H NMR spectroscopy reveal the existence of an asymmetricprotonated water trimer, H7

+O3, in acetonitrile. The core H7+O3

motif persists in larger protonated water clusters in acetonitrileup to at least 8 water molecules. Quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD)simulations reveal irreversible proton transport promoted bypropagating the asymmetric H7

+O3 structure in solution. TheQM/MM calculations allow for the successful simulation of themeasured IR absorption spectra of H7

+O3 in the OH stretch

region, which reaffirms the assignment of the H7+O3 spectra to

a hybrid-complex structure: a protonated water dimer stronglyhydrogen-bonded to a third water molecule with the protonexchanging between the two possible shared-proton Zundel-like centers. The H7

+O3 structure lends itself to promotingirreversible proton transport in presence of even one additionalwater molecule. We demonstrate how continuously evolvingH7

+O3 structures may support proton transport within largerwater solvates.

1. Introduction

Proton solvation in aqueous solutions is paramount forcomprehending countless proton transfer reactions andproton transport processes.[1] The four smallest protonatedwater clusters identified in the gas phase by their distinctiveIR absorption spectra are H3

+O, H5+O2, H7

+O3 and H9+O4.

[2]

The solvation patterns of the proton in the liquid phase arefluxional and are difficult to assign to specific geometricstructures of the aqueous proton[3] because of the fluctuatingsolvent environment and active proton transport whichcontinuously affect its aqueous environment.[4] In this study,we probe small protonated water clusters in liquidacetonitrile (ACN)[5], a polar hydrogen-bonding-accepting(HBA) solvent. ACN exhibits ultrafast solvent relaxation timescomparable to that of liquid water[6] and mixes with water inall proportions. In ACN/H2O mixtures the proton residesexclusively in the aqueous portion of the mixtures and theprotonated water solvates are stabilized from the outside bythe ACN solvent because water is a much better solvent forthe proton.[4e–h,5] Importantly, ACN does not protonate toACNH+ in presence of water as H3

+O is a much weaker acidthan ACNH+ : pKa(ACNH+)�� 10, pKa (H3

+O in ACN)=2.2.[7]

We introduce protons to ACN/H2O solutions by very strongmineral acids such as CF3SO3H, HClO4 and HI which dissociatein ACN/H2O solutions.:[4e,5,8] the pKa’s of CF3SO3H, HClO4 and HIare ~2–3 in dry ACN.[4e,5,8,9]

The mineral acids become much stronger acids inpresence of even traces of water. Here, we mainly use triflicacid CF3SO3H and we use the IR absorption of its S� O stretchvibration to report directly on the acid protonation state(Figure 1).

[a] E. Kozari, Dr. M. Sigalov, Dr. D. Pines, Prof. Dr. E. PinesDepartment of ChemistryBen-Gurion University of the NegevP.O. Box 653, Beer-Sheva, 84105, IsraelE-mail: epines@bgu.ac.il

[b] Dr. B. P. FingerhutMax-Born-Institut für Nichtlineare Optik und KurzzeitspektroskopieBerlin 12489, Germany

© 2021 The Authors. ChemPhysChem published by Wiley-VCH GmbH.This is an open access article under the terms of the Creative CommonsAttribution Non-Commercial NoDerivs License, which permits use anddistribution in any medium, provided the original work is properly cited,the use is non-commercial and no modifications or adaptations aremade.

Figure 1. IR absorption of the S� O stretch vibration of 0.6 M triflic acidCF3SO3H as a function of the H2O/acid molar ratio x in CD3CN. The peak ofthe S� OH absorption of the acid is at 1413 cm� 1 and the peak of the IRabsorption of the deprotonated triflate anion CF3SO3

� is at 1322 cm� 1 (frombottom to top: x=0.02, 0.053 0.12, 0.22, 0.52, 0.62, 0.82, 0.92, 1.02). The acidis fully dissociated at roughly 1 :1 acid-to-water ratio: x=1.02. Inset: A linearcorrelation is found between x and the fraction of the dissociated acid in therange 0.02�x�1. Color coding is for guiding the eye as x varies.

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2. Results and Discussion

The IR and NMR spectra of ‘free’ water (Figures 2A, B)considerably change for protonated water as a function ofthe water-to-acid ratio x= [H2O]/[H+ ] indicating the strongeffect of the proton on the H2O molecules directly solvatingit (Figures 3A–C). The spectral changes in our experimentswere found to only depend on x and not on the absoluteconcentrations of water indicating that the observed effectsare not due to macroscopic dielectric changes in the solvent.In presence of the proton, the absorption of the OH stretchof the water molecules solvating the proton shifts to the redby about 200 cm� 1, becomes much wider and loses thedistinction between the asymmetric and symmetric OHstretch vibrations. Concomitantly, the 1635 cm� 1 bend-tran-sition becomes much wider and moves to the blue by about100 cm� 1 typical of water molecules solvating the proton in ashared-proton Zundel configuration, H5

+O2. The 1635 cm� 1

bend-transition typical of water molecules not stronglyinteracting with the proton is clearly evident on top of theZundel absorption for x�2.2 but the red-edge of the OHstretch does not resemble the absorption of free water evenfor x=3.9.

The solvent perspective complements the solute perspec-tive of the protonated water clusters shown in Figure 3. TheCN triple-bond stretch vibration centered in neat CD3CN at2262 cm� 1 reports on the average proximity of the CN groupsto the proton: the closer the electron-rich CN triple-bond isto the proton positive charge the more its absorption blue-shifts.[10] When CN groups solvating protonated water-clusters in ACN are replaced by additional water moleculesthey move away from the proton and their absorptions red-shift toward their absorption in neat ACN. We thus use theCN stretch as a spectator for the average size of the

protonated water clusters which are embedded in ACN.Preparing solutions with larger x values results in an increasein the size of the water solvates and in the absorption of theCN groups less affected by the hydrated proton (Figure 4).

Figure 4 shows four apparent isosbestic points at2296.5 cm� 1, 2282 cm� 1, 2275 cm� 1 and 2273.5 cm� 1 that weassign to population transitions between CN groups with IRabsorpions centered at 2299 cm� 1, 2288 cm1, 2278.5 cm� 1,2272 cm� 1 and 2268 cm� 1. In harmony with the soluteperspective of Figure 3 we assign these absorption peaks toCN groups solvating size-distinctive protonated-water sol-vates. As x increases in the range of 0� x�6 the absorptionof the CN stretch red-shifts and we reconstruct the IR spectraby assuming population transitions between CN groupssolvating distinctive protonated water clusters which areaffected by x. Importantly, the narrow size-distribution of theprotonated water clusters that we find from the analysis ofthe spectator CN-stretch absorption (Figure 4) and the onewe find using the IR absorption of the solute OH stretch,shown in Figure 3, are in full agreement with each other,Figure 5.

Figure 5 clearly indicates that the spectroscopic dataemerging from the solvent perspective on the size distribu-tion (cluster-size speciation) of small protonated watersolvates in acetonitrile coincides with the size-distributionprovided by the solute perspective. Put together, the fullagreement between the two independent observationsallows us to unequivocally determine the average size of theprotonated water solvates in acetonitrile. The cluster-sizeanalysis is further corroborated by NMR spectroscopy doneon the same solutions (see below).

We next focus on water/acid solutions in the compositionrange 2.2�x�2.9 (Figure 3B). At this solution compositionrange the average size of the protonated water solvates

Figure 2. A) The FTIR spectra of unprotonated (‘free’) water solvated in CD3CN taken at the indicated concentrations. The bend transition of unprotonatedwater appears as a relatively narrow absorption at 1635 cm� 1 and the OH stretch vibration shows a separation between the symmetric and asymmetricvibration in H2O peaking at 3540 and 3620 cm� 1 respectively. B) The chemical shifts δ1HTMS (H2O) of 0.6 M, 1.2 M and 1.8 M of ‘free’ water in CD3CN solutionswhose IR absorption is shown in (A). The average chemical shift of the two H atoms in H2O are at δ1HTMS=2.29, 2.45 and 2.58 ppm respectively whichindicates a small degree of water-water association which slightly increases as a function of the water concentration, δ1HTMS of traces of largely unassociatedH2O in ACN=1.92. The corresponding chemical shifts of 0.6 M, 1.2 M and 1.8 M of protonated water protonated with 0.6 M CF3SO3H appear at much lowerfields5.

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changes from 2 to 3 water molecules and involves the transitionfrom H5

+O2 to H7+O3 solvates and the solutions are practically

made of mixtures of the Zundel cation H5+O2, its IR absorption

fully characterized in our previous work,[4f–h] and (H2O)3H+

solvates which we identify below as the asymmetric H7+O3

complex. The cluster-size speciation based on the IR absorptionof the clusters was made assuming 50% population of H7

+O3 atthe x=2.5 composition with 5% uncertainty. The speciationwas further verified independently by analysing the absorptionof the CN stretch, Figure 4 and the average chemical shift of thesolutions, Figure 6. We reconstruct all chemical shifts in thecomposition range 2.2<x�2.8 assuming it is a weightedaverage of the chemical shifts of H5

+O2 and H7+O3 their

contribution to the total cluster population changing linearly inthis range to 80% of H7

+O3 and 20% of H5+O2, see eq. 1 and

Figure 6B. Expanding on our NMR experiment we note thatprotons exchange much faster than the time-scale of themeasurement which results in observing a single averagedchemical shift. Under fast-exchange conditions NMR measures asingle chemical shift δ1Hav

[11] averaged over all exchangeable Hatoms in the protonated water solvates and over the two Hatoms of any ‘free‘ water which exchange H-atoms with theprotonated water solvates if such water molecules exist in theinvestigated ACN solutions. Based on the IR and NMR spectra(Figures. 3, 6) we conclude that the solutions are composed ofH5

+O2 and H7+O3 solvates with no ‘free’ water and that their

Figure 3. The IR absorption spectra for protonated water in acetonitrile. The broken lines are the generated spectral fits of the measured spectra, full lines. Thespectral fits are practically indistinguishable from the measured ones. A) Measured IR absorption spectra for solution compositions of 1.1 <x<1.9 showingthe gradual transition between H3

+O to H5+O2 complexes. The two limiting structures are marked in blue (H3

+O) and red (H5+O2). Measured spectra were

fitted assuming a linear combination of the two limiting structures with relative populations obeying the stochoimetric water-to-acid ratio x and undergoing atwo-state transition as a function of x.[4f] B) Top: IR absorption in the OH stretch and the water-bend regions for solution compositions (lower curves to top)x=2.3, 2.5, 2.7, 2.9 which is the solution composition range where the transition from H5

+O2 to H7+O3 occurs. Bottom: Difference spectra between the IR

absorption of about 90% H7+O3 measured in x=3 solutions (dark-red) and H5

+O2 (red-line) highlighting an apparent isosbestic point at 3200 cm� 1. In therange 2�x�3 the water bend transition is apparent only above about x=2.2. However, our experimental error makes this determination uncertain. C)Absorption spectra for (bottom to top): x=3.2, 3.4, 3.6, 3.9 solutions showing no isosbestic point. The core absorption of H7

+O3 is the most-lower (purple) lineand remains invariant upon further increase in the average size of the protonated water solvates. Bottom: The difference spectra between the upperabsorptions and the bottom absorption of H7

+O3 results in a water-like absorption spectrum marked by H2O*, considerably different from the spectra of ‘free’water shown in Figure 2A. The vertical line indicates the water-bend transition at 1635 cm� 1. D) Analysis of the amplitude of the 1635 cm� 1 transition as afunction of x. We detect the bend-transition for x >2.2 and the correlation appears to approach linearity for x>2.6 extending into water clusters larger thanH7

+O3. Comparing between C and D, the observed O.D. change at the bend-transition between x=4 and x=3 solutions is about 50% larger then the O.D.change between x=3 and x=2 solutions. The black curved line is meant to guide the eye, error bars are empiric and are based on the spread in the outcomeof multiple sets of experiments.

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relative abundance changes linearly as a function of x. Thisgives rise to an average chemical shift which is calculated inFigure 6 B for x=2.4, 2.6, 2.8 solutions according to a two-populations distribution [Eq. (1)]:

d1Hcalc ¼ ðd1HavðH5

þO2Þ*5*d2þ

d1HavðH7þO3Þ*7*d3Þ=ð5*d2 þ 7*d3Þ

(1)

We use δ1Hav(H5+O2)=9.5, and δ1Hav(H7

+O5))=8.3. d2 andd3 are the molar fractions of H5

+O2 and H7+O3 respectively

which are directly determined from the value of x. Todetermine the values of the chemical shifts of the x=2, 2.2and x=3 solutions we use the full speciation that is derivedfrom our analysis of the OH and CN absorption spectra shownin Figure 5 which also involves averaging the weightedchemical shifts of H3

+O and the protonated water tetramerH9

+O4 which were determined separately.[5] We find analmost perfect correlation between the calculated and themeasured δ1Hav values. The experimental δ1Hav(H7

+O3) value8.3 is in excellent agreement with the average theoreticalchemical shift of H7

+O3 in Ref. 5, δ1Hav =8.35, which is theaverage δ1Hav(H7

+O3) value of the symmetric (8.58) andasymmetric (8.12) H7

+O3 complexes in acetonitrile.[5] Such agood agreement is only possible for a system were all watermolecules are protonated and in the form of either H5

+O2 or(H2O)3H

+ because the chemical shift of ‘free‘ water (Fig-ure 2B) is too small to be accommodated by Eq. 1. Con-sequently the theoretical δ1Hav calculations were done forpure H7

+O3 with no ‘free’ water.[5]

Summarizing our experimental findings, we concludethat: (1) all water molecules in our experiments directlysolvate the proton with practically no ‘free’ water up to atleast x= [H2O]/[H+ ]=4; (2) the size-distribution of smallprotonated water solvates in acetonitrile (H2O)nH

+, n=1,2,3,4is narrowly distributed around the average number of watermolecules per proton, i. e., around x.

2.1. Infrared Fingerprint of H7+O3 Solvates

Our 3-pronged experimental approach unequivocally demon-strates the existence of small protonated water solvates inacetonitrile. In particular, we are able to determine with highcertainty for the first time the IR absorption spectra of theprotonated water trimer in these solutions. In Figure 7, the IRabsorption spectra between 1500–3750 cm� 1 are comparedfor CF3SO3H and HClO4 acid using x=3 solutions containingabout 90% of all protonated water clusters in the form of H7

+

O3 in CD3CN.The two practically identical IR absorption spectra consist

of a blue-shifted water-bend transition at 1735 cm� 1 assignedto the two water molecules in H5

+O2[4] and a very weak

much-narrower bend-transition at 1635 cm� 1 resembling‚“free” H2O in CD3CN but having a much weaker opticaldensity than the optical density of the “free” water-bendtransition measured at the same water concentration.Evidently, the difference in the two acid-anions do not causea considerable change in the IR spectra of the protonatedwater solvates. NMR spectroscopy and the CN absorption ofthe solutions demonstrate that the 1635 cm� 1 transitionshown in Figure 7 belongs to water molecules that are partof the protonated water trimer, otherwise the measuredaverage chemical shifts and the displayed blue shifts in theCN stretch vibration would have been much smaller. In theOH stretch region, the spectrum in 2� x�3 does not closelyresemble either the protonated water dimer, the spectrum of“free” water or any weighted combination of the two,

Figure 4. The CN triple-bond absorption as a function of the water-to-acidmolar-ratio x= [H2O]/[H+]. The spectral-shifts of the CN triple-bond oscillatorare sensitive to the proximity of the CN group to the proton charge andrespond by red-shifting to the increase in the size of the protonated watersolvates as x increases, see text.[10] n is the order of the water solvate asreported by the CN.

Figure 5. A comparison between the solute-side view reported by the OHstretch (red lines) and the solvent-side view reported by the CN stretch (bluelines) of the size-distribution of small protonated water-clusters inacetonitrile as a function of x, the solution composition, in the range0�x�3. The analysis of the OH stretch absorption is based on Figure 3A,Band the analysis of the CN stretch is based on Figure 4. The two cluster-sizedistributions are in full harmony with each other. n indicates the order of theprotonated water clusters and the relative normalized abundance of then=0, 1, 2, 3 clusters are given as a function of x.

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Figure 3B. We thus assign the spectrum in Figure 7 to ahybrid complex of protonated water, a protonated watersolvate which is a combination between the Zundel cationH5

+O2 and a single, strongly H-bonded water molecule. Thestrong H-bonding interactions modify both spectra. Weidentify this hybrid protonated water complex having the(H2O)3H

+ stoichiometry with the fully solvated H7+O3 com-

plex in acetonitrile. Unlike in the gas phase,[2] where theprotonated water trimer is symmetric, in solution we expectthe very rapidly fluctuating electric field of the solvent toinduce an asymmetric distortion of the structure. An asym-metric distortion is apparent in the IR spectra of the complexin the OH absorption region and also comes about in ourQM/MM simulations.[4h]

Further support for our structure assignment of the(H2O)3H

+ solvate to an asymmetric H7+O3 complex is given

by the IR absorption in the shared-proton region 1150–1450 cm� 1. Using HI as the proton source allows to directlyaccess this region because the acid anion, I� , does not absorbin this region. We find that in the shared proton region theabsorption of H7

+O3 resembles the shared-proton absorptionof H5

+O2 (Figure 8). The shared proton band slightly blue-shifts from 1145 cm� 1 (H5

+O2) to 1160 cm� 1 (H7+O3) and has

about 15% larger spectral width at FWHM. The absorption ofHI in bulk water further blue-shifts to 1205 cm� 1 and has apractically identical spectral width at FWHM to that of H7

+O3

(Figure 8).[4g]

Figure 6. A) The measured average chemical shifts δ1Hav of 0.6 M CF3SO3H in CD3CN solutions in the range 2.2�x�2.8 (0.6 M acid in 1.3–1.7 M H2O) atT=293 K, see also Figure 2B to compare with the chemical shifts of unprotonated ‘free’ water at similar concentrations. B) Comparison between theexperimental chemical shifts δ1Hav and the calculated δ1Hcalc values (eq. 1) assuming the solution is composed of only H5

+O2 and H7+O3 solvates without any

‘free’ water. The relative abundance of the two protonated water solvates changes as a function of x and confirms to the population distribution shown inFigure 5.

Figure 7. IR absorption of largely (90%) H7+O3 solvates in CD3CN using 0.6 M

CF3SO3H or 0.6 M HClO4 each with 1.8 M H2O (x=3) showing the OH stretchand water-bend 1500–3750 cm� 1 regions. The weak ‘free-water’-like bend-transition is indicated by the vertical line, however the NMR spectra of thesolutions indicate that there is no ‘free’ water in these solutions.

Figure 8. IR spectra of 0.6 M HI in ACN in the shared-proton region 1000–1450 cm� 1 for the indicated protonated water solvates and for 0.6 M HI inpure water. The wavelengths of maximum absorptions are indicated abovethe curves.

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2.2. Quantum Mechanical/Molecular Mechanical MolecularDynamics Simulations

Quantum mechanical/molecular mechanical molecular dy-namics (QM/MM-MD) simulations carried out for an extendedtrajectory4h were performed to analyze the structure andelectric field induced distortions and proton-translocationdynamics of H5

+O2, H7+O3 and H9

+O4 solvates in fluctuatingenvironment of ACN solvent at ambient conditions (T=

300 K). The extended long-time trajectory data exceeding0.5 ns (simulation time of 547.58 ps for H9

+O4, see Computa-tional Details) allows insight into the H7

+O3 to H7+O3 proton

transport dynamics in the H9+O4 unit (see below). QM/MM-

MD simulations utilize hybrid density functional SOGGA11-X[12] for the QM region. SOGGA11-X/aug-cc-pVTZ level oftheory accurately reproduces highest level, wave-functionbased coupled-cluster benchmark data and previous QM/MM-MD simulations of H5

+O2 were able to provide infraredabsorption spectra of H5

+O2 in the shared-proton region1150–1450 cm� 1 in good agreement with the experiment.[4g]

Our current QM/MM-MD approach is benchmarked viathe simulated IR spectra in the OH absorption region of H5

+

O2 and H7+O3 (Figure 9) that can be directly compared to our

experimental spectra (Figures 3A, B). We find generally goodagreement in the peak positions and width of the OHabsorption region of H5

+O2 and H7+O3 compared to the

experiment (peak positions: 3270 cm� 1 vs ~3300 cm� 1 forH5

+O2 and 3350 cm� 1 vs ~3375 cm� 1 for H7+O3). Moreover,

the QM/MM-MD approach faithfully reproduces the higherintensity of H5

+O2 in the 2700–3200 cm� 1 region while forH7

+O3 the much higher intensity in the 3400–3500 cm� 1

range is also reproduced. We conclude that the QM/MM-MDmethod applied on intact H5

+O2 and H7+O3 structures show a

satisfactory agreement with the main features of the exper-imental spectra in the OH absorption region (Figure 3B). Thecomputational model thus provides a reasonable descriptionof both structural and electronic changes accompanying theinteraction of H5

+O2 with the additional water molecule in

the H7+O3 complex subject to the electric field fluctuations of

the ACN environment.Figure 10 presents the potential of mean force of proton

translocation in molecular chains of four water moleculesand an excess proton (H9

+O4). The elementary steps leadingto H7

+O3 to H7+O3 proton transport are proton translocation

within the H7+O3 motif of the H9

+O4 chain (Figure 10A) andthe rearrangement of hydrogen bond network within H9

+O4

(Figure 10B). As reported before,[4h] QM/MM-MD simulationscapture the unique structural properties of the H7

+O3 motif.The fluctuating solvent field induces a prevailing solvationstructure of a dimeric H5

+O2 unit for the excess proton thatgives rise to the characteristic proton transfer mode in the~1200 cm� 1 region.[4g,h] The particularly strong hydrogen-bond of the dimeric proton-harboring H5

+O2 unit withinH7

+O3 has a median O···O distance R1 =2.46 Å, only about0.05 Å larger than in the gas phase. The dimeric unit ispreserved in the larger water solvates including the star-likestructure of H9

+O4. The shortest hydrogen bond R1 frequentlyexchanges with one of the closest water neighbors (medianO···O distance R2~2.55 Å) together forming the H7

+O3 com-plex. Translocation of the shortest hydrogen bond R1 withinH7

+O3 which switches the location of the dimeric protonproceeds without contraction of the H7

+O3 motif (Fig-ure 10A). This scenario results in reversible proton trans-location within the 3-oxygens arrangement of the H7

+O3 uniton a typical ~150 fs timescale. A similar timescale has beenrevealed in time-resolved anisotropy measurements whichare sensitive to changes in directionality of the vibrationaltransition dipole moment.[13]

Figure 10B shows the H7+O3 to H7

+O3 proton trans-location in the H9

+O4 chain-solvate in ACN. The QM/MM-MDsimulations demonstrate irreversible proton translocationalong a minimal 4 water-molecule arrangement embedded inACN. Rearrangements of hydrogen bonds in the 3-foldhierarchical hydrogen-bond network around the active pro-ton, marked as hydrogen-bonds R1, R2 and R3 in Figure 10A, B,drive trimer-to-trimer proton transport. The 2-fold hydrogen-bond length-hierarchy of the H7

+O3 motif in ACN is preservedin the larger H9

+O4 solvate. The 3rd hydrogen-bond to the 4thwater molecule R3 is considerably weaker for both the star-and chain-like arrangements of H9

+O4 (median O� O distanceR3 ~2.63 Å). This creates an intrinsic three-fold hierarchy ofhydrogen-bonds in the protonated tetramer not observed ingas-phase simulations. The compression of the collectivehydrogen bond coordinates R2 +R3 and correlated displace-ment along symmetrized proton transfer coordinate (z2+

z3)/2 characterize the structural changes upon rearrange-ment of the hydrogen bond network that are required fortranslocation of the H7

+O3 motif within the H9+O4 chain and

thus causing irreversible proton transfer within the chain.Such rearrangement of hydrogen bond network within thefour-water molecular chain is rate determining in ACNenvironment with a free energy barrier of ~421�53 cm� 1

(1.2�0.15 kcal/mol). Structurally, translocation of the H7+O3

is accompanied by an effective O···O contraction along thechain by about 0.3 Å.

Figure 9. Simulated H5+O2 (red) and H7

+O3 (blue) IR spectra obtained fromquantum mechanical/molecular mechanical-molecular dynamics (QM/MM-MD) simulations via the Fourier transform C(ν) of the respective dipolemoment autocorrelation function C(t) (see Computational Details). SimulatedIR spectra were normalized to the experimental isosbestic point at3200 cm� 1 (Figure 3B).

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The QM/MM-MD simulations, supported by our exper-imental findings of the IR fingerprint of the H7

+O3 motif,suggest a picture where a fluctuating asymmetric hybridstructure made of a shared-proton unit H5

+O2 stronglyinteracting with a 3rd water molecule mediates proton trans-port via structural diffusion, the so-called Grotthussmechanism.[1f,14] Persistent translocation of the protoncharge,[14,15] i. e., irreversible proton-transport results fromtranslocating the H7

+O3 unit by one water molecule and isdriven by fluctuations in the unit’s 1st solvation shell (Fig-ure 11). Such rearrangements shift the center of the trimericstructure from O2* to O3*. The newly formed H7

+O3 unit(oxygens O2� O3*� O4) shares 2 water molecules with theH7

+O3 unit which preceded it (oxygens O1� O2*� O3).Adopting a general reaction model by Hynes et al.,[16]

water-water hydrogen-bond rearrangement is likely to beclocked by large amplitude angular jumps which results inrotational-like orientational rearrangements of the surround-ing water molecules on a typical timescale of 1 ps (pictoriallyindicated by an arrow in Figure 11).

The translocation of the H7+O3 motif is step-wise and

allows persistent transport of the proton tightly coupled to~ps hydrogen-bond angular rearrangements. It should benoted that in this suggested scenario of proton transport, the3-fold hydrogen-bond hierarchy in the protonated waterspecies is preserved with no transient production ordestruction of monomeric H3

+O. Our QM/MM simulationsimply that the transition-state for proton transport inaqueous solutions is likely to be associated with the trans-location of the H7

+O3 motif coupled to transient rearrange-ments of hydrogen-bonds in the trimeric-unit’s 1st solvation-shell water molecules in what may be described as streamingH7

+O3 to H7+O3 transitions.

3. Conclusions

Our IR and NMR studies have revealed the spectroscopicfingerprints of the core solvation motif, H7

+O3, of thehydrated proton in ACN/water solutions. QM/MM simulationsshow that the dimeric shared-proton structure is preserved in

Figure 10. Potential of mean force of proton translocation in molecular chains of four water molecules and an excess proton (H9+O4): A) Reversible proton

translocation within the H7+O3 motif is accompanied by fluctuating H-bonding interactions with a 4th water molecule. B) Rearrangement of hydrogen bond

network within H9+O4 drive irreversible proton transport by translocating the H7

+O3 unit to a new site with a different geometry. (A) and (B) form theelementary steps of the trimer-to-trimer (T� T) proton transport mechanism. z1, z2 and z3 denote proton transfer coordinates z= rOi···H+ � rOj···H+ (rOi···H+ andrOj···H+ are distances between H+ and the oxygen atoms of flanking water molecules i and j, respectively) for shortest, second shortest and third shortest O···Odistances R1, R2 (A) and R2, R3 (B), respectively. In the limiting geometry of a symmetric dimeric H5

+O2 motif, the proton resides at equal distances from thetwo oxygen atoms (z=0). The symmetrized proton transfer coordinates (z1+ z2)/2 and (z2+z3)/2 indicate proton translocation within H7

+O3 and H9+O4

motifs, respectively, and the sum of hydrogen bond coordinates R1+R2 and R2+R3 characterize structural changes. The low correlation of symmetrized protontransfer coordinate (z1+ z2)/2 and the sum of hydrogen bond coordinates R1+R2 (A) reflect the minor structural changes of the H7

+O3 motif upon reversibletranslocation of the active proton within H7

+O3 on the ~150 fs timescale.

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fluctuating H7+O3 units and suggest it has a central role in

structural proton translocation along water chains. Thehybrid structure of H7

+O3 enables-by the merit of its uniquehybrid structure-persistent proton transport. It is likely totake part in proton transport through bulk water viastructural diffusion, which requires persistent translocation ofthe proton charge driven by the breaking and formation ofhydrogen bonds.[14,15]

Methods Section

Experimental Details

Sample preparation

Solution preparation was done in a home-made glob-box underdry Ar atmosphere to minimize the water content in theacetonitrile solution. Anhydrous CD3CN 99.8% (Sigma-Aldrich),and CF3SO3H (triflic acid) 99% extra pure (Strem Chemicals) wereused as received. HClO4 (Sigma-Aldrich), was 70.7% by weight(x=H2O/acid=2.3) and was further concentrated down to aboutx=1.3 by drying the concentrated acid in acetonitrile solutionsusing P2O5 as the drying agent. HI (Merck) was 67% by weight(H2O/acid=3.5) and the acid was further dried by P2O5 inacetonitrile solutions down to about x=1.8.

Infrared spectra measurements

Steady state IR spectra of 0.6 M or 0.5 M of the acids in CD3CN,were carried out with CaF2 windows using optical path lengths of15 and 25 μm.

The measurements were done with Nicolet IS10 FTIR instrumentwith 0.4–1 cm� 1 resolution while applying constant dry N2 flowto keep moisture out of the surrounding atmosphere. The dataas shown represent the average of 20 FTIR absorption scans aftersubtraction of the absorption of the pure CD3CN solvent.

1H NMR experiments1H NMR experiments were carried out using BrukerBiospin GmbH400 MHz spectrometer of 0.6 M solutions of triflic acid indeuterated acetonitrile (CD3CN). The measurements were donein a sealed NMR tube, temperature stabilized and cooled byliquid nitrogen. The residual 1H impurity signal of CHD2CN inCD3CN solvent (δ 1H=1.94 ppm on the TMS scale) was used asthe NMR standard chemical-shift.

Computational Details

Quantum Mechanical/Molecular Mechanical MolecularDynamics Simulations

QM/MM-MD simulations are employed to simulate the dynamicsof protonated water tetramer cluster H9

+O4 in fluctuating ACNsolvent at ambient conditions (T=300 K) and follow theprocedure detailed in Refs. [4 g,h]. The QM/MM treatment utilizeshybrid density functional SOGGA11-X (Ref. [12]) that is able toprovide infrared absorption spectra of H5

+O2 in ACN in theshared-proton region in good agreement with the experiment.[4g]

The use SOGGA11-X/aug-cc-pVTZ level of theory reproduceshighest level, wave-function based coupled-cluster singles-doubles with perturbative triples corrections (CCSD(T)/aug-cc-pVTZ) potential and shows excellent performance for barrierheights, the energetic position of minima for varying O1···O2

distances R1 in H5+O2 and equally good performance for the

variation of O2···O3 (R2) in H7+O3, i. e., the coordinate of a third

water molecule approaching interacting with H5+O2.

The QM/MM-MD simulations have been performed with a locallymodified version of the AMBER14 program package[17] extendingthe mixed quantum-classical (QM/MM) module14[18] to the Molproprogram package[19] as external quantum chemistry program. QMcalculations of the solvated excess proton with two (H5

+O2),three (H7

+O3) and four water molecules (H9+O4) have been

performed on density functional level of theory with the hybridGGA functional SOGGA11-X[12] employing density fitting.[20] Watermolecules together with the excess proton H+ were entirelytreated on QM level. The comparison of the OH absorptionregion of H5

+O2 and H7+O3 uses trajectory data of Refs. [4 g,h] for

Figure 11. A pictorial sketch of the H7+O3 complex (blue coloring) in solution allowing for proton translocation by random fluctuations in the H-bonding

interactions with its surrounding water molecules drawn for a [H2O]/[H+]=8 solvate. The trimer -to-trimer proton transport mechanism is highlighted by theorange color. The active proton is indicated in red and its irreversible translocation via the H7

+O3 unit is driven by random fluctuations in the position of thefive water molecules directly solvating the H7

+O3 unit marked in green. R1 is the dimeric (shortest) O� O separation within the H7+O3 complex which migrates

by one water molecule as the proton translocate, R2 is the 2nd (intermediate) O� O separation distance within the H7+O3 complex and R3 is the longest O� O

separation distance between O3 of the H7+O3 unit and one of its solvating water molecules approaching O3.

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simulation of spectra via the Fourier transform C(ν) of the dipolemoment autocorrelation function C(t) (Figure 9). Simulated infra-red absorption spectra in the OH stretch region were smooth-ened via 72 frequency-step moving average. Insight into thetrimer-to-trimer proton translocation mechanism in H9

+O4 (Fig-ure 10) is provided via a new extended trajectory data set of547.58 ps simulation time for H9

+O4.

The protonated water clusters were placed in a rectangular boxof acetonitrile molecules (1180 acetonitrile molecules, boxdimension: 45.742×55.084×55.084 Å) employing periodic boun-dary conditions. Acetonitrile molecules were treated on themolecular mechanics (MM) level with force field parameters ofthe rigid body united atom model taken from Ref. [21]. The rigidbody united atom model reproduces dynamic properties like thesolvation correlation function with good accuracy.[22] Triflate(CF3SO3

� ) counter ion (force field parameters and partial chargestaken from Ref. [2123]) was employed for charge neutrality.Long-range electrostatic interactions within the MM region weretreated with the particle mesh Ewald (PME) approach with realspace cut-off (10 Å). Electrostatic embedding in the QM Hamil-tonian was performed by including the partial charges ofacetonitrile molecules within a cut-off radius Rc =10 Å of the QMregion.

Classical equation of motion in QM/MM-MD simulations werepropagated with a time step of Δt=0.25 fs. The system wasinitially minimization on the QM/MM level for 3500 steps.Equilibration was performed by heating the system to 100.0 Kduring a short 10 ps trajectory performed in the nvt ensemble(Langevin dynamics with 1.0 ps� 1 collision frequency) followedby further equilibration in the npt ensemble at 300 K for 60 ps(1.0 bar reference pressure). During npt equilibration, the densityconverged to 0.7469�0.0015 g/cm3 in reasonable agreementwith the experimental value (0.7768 g/cm3). Equilibration wasperformed with position constraints (5 kcal/mol) on the QM-region to avoid a disintegration of the H9

+O4 cluster. Startingfrom the corresponding equilibrated configurations, long nvtQM/MM trajectories were simulated where the position restraintswere gradually weakened (5 kcal/mol!0.2 kcal/mol). Productionsimulations were launched without position restraints every20 ps from the weakly constrained trajectory. A reduced aug-cc-pVDZ basis set for the QM region was used for equilibration andproduction simulations without position constraints employedaug-cc-pVTZ basis set (391 contracted basis functions for H9

+O4).To provide a balanced description of different star like (resem-bling Eigen-type structures) and wire configurations of H9

+O4

(E� H9+O4 and W� H9

+O4, respectively) two equilibration trajecto-ries were simulated with position constraints around respectiveE� H9

+O4 and W� H9+O4 structures. The extended production run

trajectory data amount to 547.58 ps simulation time for thewater cluster H9

+O4 in the nvt ensemble at 300 K. Coordinateswere saved every 2.5 fs for further investigation. Trimer-to-trimer(T� T) proton transport along a four-water-molecule path wasinvestigated for the protonated tetramer with chain configura-tion W� H9

+O4 that accounts for 207.95 ps of the total simulationtime (Figure 10B).

Shortest, second shortest and third shortest O···O distances R1, R2

and R3, were determined via a 40 time-step moving average (~2O···O oscillation periods) of coordinates ROiOj. The procedurefollows the character of O···O hydrogen bonds but allows forshort-time (<1 O···O oscillation period) inversion of R1, R2 or R3,thus giving rise to hierarchical and overlapping distributions ofO···O distances.[4h] We have verified that the results are un-changed for varying moving averages in the range 20–80 timesteps.

Acknowledgements

E.P. acknowledges the support by the Israel Science Foundationgrant #1587/16. B.P.F. gratefully acknowledges support throughthe Deutsche Forschungsgemeinschaft within the Emmy NoetherProgramme (grant FI 2034/1-1). This project has received fundingfrom the European Research Council (ERC) under the EuropeanUnion’s Horizon 2020 research and innovation programme (grantagreement No 802817).

Conflict of Interest

The authors declare no conflict of interest.

Keywords: hydrated proton · trimer · Zundel cation · CNstretch · molecular dynamics simulations

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Manuscript received: December 28, 2020Revised manuscript received: February 13, 2021Accepted manuscript online: February 17, 2021Version of record online: March 23, 2021

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